The Theoretical Defects in DRIS and
the Restructuring of a new Approach

LI Jian and LI Mei-gui
(The Fruit Station of the Department of Agriculture of Fujian，Fuzhou 350003,P.R.China)

Abstract: There are two kinds of theoretical defects export in the Diagnosis and Recommendation Integrated System (DRIS): the distribution of nutrient elements ratios with two normal distribution appears an abnormal distribution of positive skewness; there is a blind diagnostic area by DRIS on the occasion of the nutrient elements with equal ratios but without equal quantity. In the light of the quadratic form theory of multidimensional normal distribution and the view of balance of equal probability, the Balance Diagnosis and Recommendation Integrated System (BDRIS) was developed in this paper, which is superior to DRIS and its diagnosis method is unified to critical value diagnosis. When the correlation matrix of nutrient elements R = I（identity matrix）, i.e., the effects of elements antagonism is disregarded, BDRIS will be simplified into the critical value diagnosis. In addition, the diagnosis program written in SAS language was also provided in this paper.
Key words: Diagnosis and Recommendation Integrated System (DRIS), Balance Diagnosis and Recommendation Integrated System (BDRIS), Ponkan, balance of equal probability


In consideration of the insufficiency of the nutrient critical value diagnosis of crop leaves and in the light of the crop nutrient balance, the Diagnosis and Recommendation Integrated System (DRIS) [1] was developed by Beaufils in 1973. It has been the only crop nutrient balance diagnosis method widely used till now, and there have been quite a few articles and reviews on the application of DRIS [2 - 5]. The algebraic sum of DRIS indices is zero, so there is at least an element being deficient or excessive by DRIS. It is difficult to judge whether the nutrient element is deficient or excessive. In order to solve this problem, the dry matter (DM) was subsumed into DRIS and a modified method (M-DRIS) [6 - 7] was developed by Walworh in 1984. It judged an element that is deficient or excessive by DM indices. To simply the calculations , the Deviation from Optimum Percentage (DOP) [7 - 8] was developed by Montaněs in 1993. The method is simple but the diagnosis to the elements in the method is independent. There is not essential difference between DOP and the critical value diagnosis. Therefore, DRIS and M-DRIS are only the integrated diagnosis methods for the crop nutrient. The chi-square ( χ2 ) test of elements ratios was conducted and the diagnosis parameters of DRIS — f（A/B） [1, 9 - 10] was calculated according to the normal theory by Beaufils and Sumner. However, in the studies of Ponkan nutrient indices by DRIS, two distributions of the nutrient elements ratios with approximately normal distribution presented the significant positive skewness, and it was easy to result in the loss of diagnosis information and formed a special blind area when using the elements ratios method. The finding puts a doubt on the reliability of DRIS, and a new method of crop balance nutrient diagnosis remedied the defects of DRIS was tried to be developed.
In addition to analyzing and pointing out the theoretical defects of DRIS, the shackles of the elements ratios method were threw, and the studies on the actual distribution law of the nutrient of Ponkan leaves were conducted by means of multidimensional normal theory, and the concept of equal probability balance status of nutrient elements was proposed, a mode of diagnosis that is superior to DRIS was developed, the difficult issue that the two methods (balance diagnosis and critical diagnosis) can not unify was solved, the relationship between elements antagonism and crop nutrient balance was explained, so as a more available method for crop nutrient balance diagnosis was proved in this paper.
1 Material and Methods
1.1 Sources of Data
1.1.1 Data of the nutrient elements of citrus leaves Data were selected from the analysis of 448 leaves (Citrus reticulate Blance c.v. Ponkan) sampled from Ponkan orchards (area ≥ 3.5 hm2) on red soil hilly land in 15 citrus producing counties (cities) such as Yongchun and so on in Fujian during 1996 — 2000. The sampling time, sampling method and the analysis of leaves were referred to reference [4]. The number of sample trees for each sample leaf ≥ 25. The leaf samples were analyzed by Fujian Research Institute of Subtropical Plants at Xiamen.
1.1.2 Quantification of the yield grade of the citrus orchards The unified quantification of the yield grade (G) of the sampled citrus orchards was conducted referring to reference [11].
1.2 Data Analysis
SAS 6.12 (Statistical Analysis System) was adopted for the analysis of data [12].
2 Results
2.1 Analysis of the Theoretical Defects of DRIS
The data of samples were divided into high-yield group and low-yield group according to the mean (ＥG/n=2.9) of the yield grade G of the sampling orchards. In order to make the nutrient elements of the high-yield group present ideal normality, 3% abnormal data was deleted in this paper. The normal tests of nutrient elements and their ratios of the high-yield group were carried out with proc univariate.
The results showed that the probability of the normal test (Prob. > W) ≥0.152 of the macro-elements N, P, K, Ca and Mg, while the microelements Cu, Zn, Fe, Mn and B trend extremely significant abnormal positive skewness as the application of the pesticide or trace fertilizer (Table 1). Therefore, only the macro-elements were studied in this paper.
2.1.1 The Probability Distribution of the Nutrient Elements Ratios The results from Table 1 also showed that all 20 items of elements ratios appeared the distribution of positive skewness (Skewness > 0), and 16 items of elements ratios are refused by the probability test of normality. Inevitably, the normal distribution of macro-elements ratios of crop leaves by Beaufils and Sumner [1,9] was put a doubt. In order to verify this doubt in theory, the general distribution p (z) of the two-dimensional normal random variable ratios z was derived in this paper (Deduction 1). The eq. (1-2), an abnormal hyperfunction was derived from p (z) in the eq. (1-1). In the function, only B* is a linear term:
B=z(aσ22 - rbσ1σ2) –raσ1σ2 + bσ12
When aσ22 - rbσ1σ2 ＞ 0 or （σ2/b）/(σ1/a)＞ r, i.e., when the cv ratios of two random normal variables > r, slope of B* > 0, which had a positive skewness influence on p (z). As –1 < r < 1, the condition of (σ2/b)/ (σ1/a)＞r was apt to be met, so the distribution of elements ratios tended to be positive skewness. When a = b = 0 in eq. (1-2), p(z) presented Cauchy distribution ( eq. ( 1-3 ) ), and its distribution function did not converge. In addition, according to the z = xj/xi (Fig. 1), the contour lines and equidistant lines of z were a variety of straight lines on the plane xixj, and will concentrate rapidly with the increase of z. It meant that the projection of equal ratio straight line of the mean（Ｅxi/xj）/n of elements ratios passing the point O on the plane xixj was not equidistant on the axis z, the upper side being larger than the lower one. Thus, the geometric drawing gave a visual explanation of the reason of the positive skewness distribution of element ratios. Based on the above analysis, it did not have any biological connotation that the significance of the variance ratio SA/SB between the low-yield orchard and high-yield orchard [1,9] as the foundation in selecting direct or inverse ratios of elements by DRIS. It is actually the result of nonlinear transformation, which was even apt to cause confusion in the selection and unification of DRIS diagnostic parameters. For example, there are C52＝10 combinations for 5 macro-elements, there are two selections with direct ratio or inverse ratio in each combination, so there are 210 = 1024 selections in diagnosis parameter.
2.1.2 Blind Area in the Diagnosis of Nutrient Element Ratios As DRIS used element ratios as the indices in measuring the crop nutrient balance, the diagnosis results would be completely the same when nutrient elements change in proportion. But do they have the same physiological meanings? To make it clarified, an equal ratio sieve was set up according to the diagnostic parameters in Table 1 and the samples with approximate element ratios in pairs without replication were sieved out. The correlation analysis (Table 2) between the DRIS integrated balance indices (mean square root of DRIS indices) and yield grade of the sample groups were carried out. The results showed that the correlations between the DRIS integrated balance indices and yield grade G appeared to change from the extremely significant correlation to non-correlation no matter whether the data used for screening had been standardized with the decrease of threshold value min, i.e., with the sample element ratios becoming approximate. There was a blind area of diagnosis in this condition. In views of that, the nutrient physiological conditions of crops are not completely the same in correspondence to the level of
nutrient elements with equal proportion but without equal quantity, and DRIS is not sensitive to these changes in this situation. It is another theoretical defect in DRIS. There was a 22% — 31% of the rate of wrong diagnosis based on the data in this study by DRIS if the ratio of threshold value min to r (W > Prob. ≥ 0.1) in Table 2, i.e., the ratio of numbers of sample of DRIS balance indices without correlation with yield grade G to total numbers of sample (98/448,137/448) are taken as the rate of wrong diagnosis, which is compatible with the 10% — 31% of the rate of wrong diagnosis by DRIS reported in the reference [10].